HELMHOLTZ ON THE CONSERVATION OF FORCE. 117 



as a matter of experience, can only appear as a change in the 

 relative position of at least two material bodies. Force, which 

 originates motion, can only be conceived of as referring to the 

 relation of at least two material bodies towards each other ; it is 

 therefore to be defined as the endeavour of two masses to 

 alter their relative position. But the force which two masses 

 exert upon each other must be resolved into those exerted 

 by all their particles upon each other; hence in mechanics we 

 go back to forces exerted by material points. The relation 

 of one point to another, as regards space, has reference solely to 

 their distance apart : a moving force, therefore, exerted by each 

 upon the other, can only act so as to cause an alteration of their 

 distance, that is, it must be either attractive or repulsive. 



Finally, therefore, we discover the problem of physical 

 natural science to be, to refer natural phaenomena back to un- 

 changeable attractive and repulsive forces, whose intensity 

 depends solely upon distance. The solvability of this problem is 

 the condition of the complete comprehensibility of nature. In 

 mechanical calculations this limitation of the idea of moving 

 force has not yet been assumed : a great number, however, of 

 general principles referring to the motion of compound systems 

 of bodies are only valid for the case that these bodies operate 

 upon each other by unchangeable attractive or repulsive forces ; 

 for example, the principle of virtual velocities ; the conservation 

 of the motion of the centre of gravity ; the conservation of the 

 principal plane of rotation ; of the moment of rotation of free 

 systems, and the conservation of vis viva. In terrestrial matters 

 application is made chiefly of the first and last of these prin- 

 ciples, inasmuch as the others refer to systems which are sup- 

 posed to be completely free ; we shall however show that the 

 first is only a special case of the last, which therefore must be 

 regarded as the most general and important consequence of the 

 deduction which we have made. 



Theoretical natural science therefore, if she does not rest con-^ 

 tented with half views of things, must bring her notions into 

 harmony with the expressed requirements as to the nature of 

 simple forces, and with the consequences which flow from them. 

 Her vocation will be ended as soon as the reduction of natural 

 phaenomena to simple forces is complete, and the proof given 



SCIEN. MEM.— .Va^ Phil. Vol. I. Part II. K 



